Decimals

Decimals are also use to name numbers between whole numbers.

Decimals are the same as Fractions with denominators that are multiples of 10.

5 tenths = 5/10 = 0.5

5 hundreths = 5/100 = 0.05

5 thousandths = 5/1,000 = 0.005

125 thousandths = 125/1,000 = 0.125

Place positions of decimals

1000s thousands	100s hundreds	10s tens	1s ones	.	0.1s tenths	0.01s hundredths	0.001s thousandths
	2	4	6	.	8	5	2

The first position to the right of the decimal point represents tenths – which is one divided into 10 parts.

The second position to the right of the decimal point represents hundredths – which is one divided into 100 parts.

The third position is thousandths – which is one divided into 1,000 parts.

The number on the third line is:

Words – two hundred forty six point eight five two

Decimal notation: 246.852

Fraction notation: 246 852/1000, or 246 and 852 thousandths

Money

A special use for decimals is how we write money numbers. We count money in dollars and cents. We use the symbol ‘$’ in front of the money decimal number.

We write the dollars as whole numbers, and the cents as a decimal number. The decimal point comes after the whole number. The cents are really hundredths of a dollar.

If a cheeseburger costs 3 dollars and 99 cents, we would write:

$ 3.99

This means 3 dollars and 99 hundredths of another dollar.

Comparing Decimal Numbers

Here are some examples of decimal numbers that are equal:

0.4 = 0.40 = 0.400 ( 4 tenths = 40 hundredths = 400 thousandths)

0.25 = 0.250 = 0.2500 ( 25 hundredths = 250 thousandths = 2500 ten-thousandths)

When comparing decimal numbers, it helps to add zeroes to the right of the last digit so that the decimal numbers you are comparing have the same number of digits to the right of the decimal point.

For example, compare 0.4 with 0.060

First change the 0.4 to 0.400

Now we can compare 0.400 and 0.060

0.400 > 0.060 since 400 is > 60

Compare 0.205 with 0. 21

First change 0.21 to 0.210

Now we can see that 0.205 < 0.210 since 205 < 210

Adding and Subtracting Decimals

You add and subtract decimal numbers the same way you add and subtract whole numbers with one additional rule:

Always line up the decimal points of the numbers so that the decimal points are in the same column. This ensures that you are adding numbers with the same place value. Sometimes, it is helpful to add zeroes to the end of a number so that all numbers have the same number of digits to the right of the decimal point.

Example: Add 3.4 + 28.76 + 0.001

	3	.	4	0	0
2	8	.	7	6	0
	0	.	0	0	1
3	2	.	1	6	1

Remember: You need to write your numbers neatly!!!

Adding and Subtracting Money

You add or subtract money numbers the same way you add and subtract decimals. Make sure you line up the decimal points neatly.

$ 235.56

-$ 55.45

$ 180.11

Percents

0.75 is read as 75 hundreths. So if 1 is divided into 100 parts, 0.75 means 75 of those one hundredth parts.

0.60 is read as 60 hundreths. Again, if one is divided into 100 parts, 0.60 means 60 of those hundredth parts.

Percent means per hundred or out of a hundred. 75% means 75 out of 100.

60% means 60 out of 100.

Summary

¾ = 0.75 = 75/100 = 75%

3/5 = 0.60 = 60/100 = 60%

½ = 0.50 = 50/100 = 50%

0.93 = 93/100 = 93%